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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (3): 67-76.doi: 10.6040/j.issn.1671-9352.4.2020.218

• • 上一篇    

基于L2,1范数和流形正则项的半监督谱聚类算法

杨婷1,2,朱恒东1,马盈仓1,汪义瑞2,杨小飞1*   

  1. 1.西安工程大学理学院, 陕西 西安 710600;2.安康学院数学与统计学院, 陕西 安康 725000
  • 发布日期:2021-03-16
  • 作者简介:杨婷(1996— ),女,硕士研究生,研究方向为机器学习. E-mail:15929121393@126.com*通信作者简介:杨小飞(1982— ),男,博士,副教授,研究方向为机器学习和粗糙集. E-mail:yangxiaofei2002@163.com
  • 基金资助:
    国家自然科学基金资助项目(11501435);西安工程大学研究生创新基金资助项目(chx2020031);安康学院专项基金资助(2019AYXNZX04)

Semi-supervised spectral clustering algorithm based on L2,1 norm and manifold regularization terms

YANG Ting1,2, ZHU Heng-dong1, MA Ying-cang1, WANG Yi-rui2, YANG Xiao-fei1*   

  1. 1. School of Science, Xian Polytechnic University, Xian 710600, Shaanxi, China;
    2. School of Mathematics and Statistics, Ankang University, Ankang 725000, Shaanxi, China
  • Published:2021-03-16

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摘要： 谱聚类算法受到相似矩阵的影响以及没有使用先验信息,使得聚类结果有很大的局限性。针对这一问题,提出了一种基于L2,1范数和流形正则项的半监督谱聚类算法。一方面借助L2,1范数的鲁棒性学习到合理的相似矩阵;另一方面充分利用监督信息,不仅指导了初始相似矩阵的构造,而且引入流形正则项去调整模型,从而改善聚类效果。实验结果表明,所提出的聚类算法在人工数据集和真实数据集上的聚类结果较其他聚类算法更加有效。

关键词: L2,1范数, 流形正则项, 谱聚类, 半监督学习

Abstract: The spectral clustering algorithm is affected by the similarity matrix and not using prior information, which makes the clustering results with great limitations. For this problem, we propose a semi-supervised spectral clustering algorithm based on L2,1 norm and manifold regularization terms. With the help of robustness in L2,1 norms, a reasonable similarity matrix is learned. In addition, full use of supervisory information not only is added in the initial similarity matrix, but also is used in manifold regularization term to adjust the model, thereby improving the clustering effect. The clustering results of the proposed clustering algorithm on artificial data sets and real data sets are more effective than other clustering algorithms in most cases.

Key words: L2,1 norm, manifold regularization term, spectral clustering, semi-supervised learning

中图分类号: 

  • TP311
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